/sci/ - Science & Math

>>16053689
R can be well defined and also exists
Debate me

>>16053689
No, he will earn the first royal cubit nft and we all be singing tetrachords in the pyramids

Some things he's write about, other things no so much.
I agree that mathematicians are taking infinity for granted and it's really caused an inbred mess.

>>16053689
>rewriting music
His Mod math is surface level as shit, literal student tier, I would literally be like Pai Mei to his ass. His dedekind cut is as arbitrary as possible, contradicting his entire philosophy of mathematics. He is intermediate at Number Theory at best! Refreshing to see an accomplished academic note the same discrepancies (Arithmatic, Metrology etc), but no...

Lastly...I could beat the shit out of him.

>>16053847
prove that it exists

>>16054430
sqrt(2) is both irrational and exists
sqrt(2) is in R but not Q
Thus some strict subset of R exists that excludes Q. Since R - Q is non empty, R exists as a distinct and non-trivial set.

>>16054719
>sqrt(2) is both irrational and exists
Define sqrt(2) and prove it exists.

>>16054719
Retard
You took "Intro to Proofs" or some other gay fake course like that, didn't you?

>>16054719
You have failed to suitably define R. Go back to your undergraduate class please.

>>16054724
What about from geometry: all squares have a diagonal. If a square has a side of length 1, its diagonal must be of length sqrt(2).

>>16054719
>sqrt(2) is in R
why?

>>16054734
Define length of a line segment.

>>16054731
Set of all converging Cauchy sequences in Q?

>>16054739
That’s outside the discussion. You define it and we’ll see if my answer fails that definition and requires a new one.

>>16054745
No it's not. Length is not a well-defined mathematical concept.

>>16054788
It is a well defined geometric concept. This is proof from geometry.

>>16054734
Pythagoras' theorem only applies to triangles that exist. Unfortunately, though one would like to believe there is such a triangle with sides of equal length, there is no reason to believe such a triangle actual exists. There is no number which solves x^2 = 2. A sequence nor some fantasy concoction such as a Dedekind cut is not a number nor is there any rigorous logical foundation for either--just wishful thinking on the part of modern mathematicians. The only thing you can do is introduce an algebraic placeholder much like one does with i for i^2 = -1 for the purpose of abstract algebra or look for a logically sound object like a matrix to represent it.

>>16054808
I’m talking about geometry. In geometry, points can have a relation of having a certain distance between them, and the distance 1 is not forbidden.

This was proof from geometry.

>>16054724
Construct a Cauchy sequence using the heron algorithm that "converges" to square root of 2. There you have it.

>>16054737
Because square root of 2 is the limit of a Cauchy sequence in Q and R is defined such that all Cauchy sequences converge. This property is called the completeness of R. Alternatively, you can introduce this property via Dedekind cuts, nested intervals or by demanding that bounded subsets of R necessarily have a supremum.

is this the pi = 4 guy?

>>16054813
>points can have a relation of having a certain distance between them
Outside of Cartesian geometry without imposing a notion of distance. Generally, there is no reason to assume a notion of distance exists. Moreover, even claiming or imposing some kind of distance does not necessarily mean it is well defined for all configurations, nor does it have to be defined.
>the distance 1 is not forbidden
This of course is not an argument against the facts that there is no square root of two and no triangle with exactly two sides of length 1.

>>16054813
Fun fact, in order to rotate the hypotenuse of a right triangle with base and height 1 onto the base, you need to construct a linear transformation that depends on the quantity you're trying to commensurate

>>16054829
>no reason to assume distance exists
This is wrong. Euclidean geometry requires a notion of distance relation between points or an axiom that necessarily implies this relation.
>no such triangle
I said square and since distance must exist in euclidean geometry, so must squares of side length 1. Never said this is empirical proof. This is proof from geometry.

>>16054833
I said a square of side length 1. The distance to be measured is that between two non adjacent corner points of the square. Points, lines, and therefore squares must exist in Euclidean geometry.

>>16054817
He's asking you to prove there is such a thing as the square root of 2. Not to invoke a circular argument in which one merely provides a series of rational numbers can be found using certain algorithms that approximately square to 2 while assuming a priori that there is such thing as a square root of 2.

And no. An algorithm is not a number.
>>16054822
Prove that the square root actually exists without invoking some dubious objects.
>R is defined such that all Cauchy sequences converge
Completeness is supposed to be a consequence of a definition. It is not part of the definition. The problem with R is that there are no logically sound definitions of a real number.
>Dedekind cuts
A convenient cope on the part of practitioners of the real number religion. It's just nonsense. Moreover, whereas with a sound definition such as that of a rational number, you cannot generate examples of real numbers and hence there is no reason to assume that the fantasy yields any numbers. In such example requires the use of Cauchy sequences outside of very special cases. However, this depends entirely on claiming that a Cauchy sequence is a number or that such a construct is meaningful.
>nested intervals
A nested intervals are just a variation on the same reasoning of a cut. Any discussion of nested intervals however eventually must revert to appealing to Cauchy sequences and requires them. Hence it cannot be a definition of real numbers.
>demanding that bounded subsets of R necessarily have a supremum
This reasoning is like claiming, "I demand to be a billionaire therefore I am one."

>>16054847
Completeness is a consequence. The definition is that R is the set of all converging Cauchy sequences. You’re misrepresenting his answer.

>>16054841
>This is wrong. Euclidean geometry requires a notion of distance relation between points or an axiom that necessarily implies this relation.
This is wrong. At a fundamental level, Euclidean geometry does not require a notion of distance nor does its axioms imply it nor does the form of geometry require any such numbers be imposed on objects. The imposition of notions of numbers called distance, area, etc. are specializations of Euclidean geometry.
>I said square and since distance must exist in euclidean geometry
It doesn't need to exist in Euclidean geometry. You are assuming additional hypotheses here.
>Never said this is empirical proof.
It's not even a logical proof.
>This is proof from geometry.
You haven't proven anything.

>>16054853
Euclidean geometry (hilbert definition) requires the notion of points, lines, planes, and three classes of relations, one of which is what we call distance (also called betweenness).

Squares are a direct result from these notions.

>>16054859
If you consider Euclid's elements, there is no assumption of distance nor the assignment of numbers to line segments. Everything is tied up in the notion of lines, points, and angles. When you read Euclid carefully, you will find that in the Greek (ignoring the impositions of translators), that there is no appeal to a number called distance or is it required. A triangle or circle is a planar object in itself. It is not the consequence of line segments.

https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

In Euclid, the point, the line, the triangle, etc. are objects in themselves and are being discussed independently of any imposition of a measurement system or attempts at measurement systems.
>hilbert definition
Let us stick to Euclid instead. You will find a distorted version of geometry if you go with Hilbert. Hilbert makes the fallacy of assuming the imposition of measurements or numbers are required

>>16054896
I don’t care about Euclid in the Greek. Hilbert is far more clear and rigorous to my mind. And distance exists in hilbert.

I accept your concession and admission of your error.

I accept your concession and admission of your error.

>>16054905
Lol. You're not talking about geometry if you pretend Hilbert's impositions are required.

>>16054919
I am talking about geometry actually. I just said it.

>>16054826
No, it's someone even dumber if you can imagine that
>not all line's have length just like all human's don't have tax returns

>>16055237
That’s so retarded. How do you define a continuous object like a line and pretend some random lengths are different? Gotta be retarded to do that. You can literally just change the units lmao

>>16054792
grug notes some sticks larger than other sticks.
modernist mathematician defines stick without stick

keep on zooming in on your 'real' diagonal of a square of side length 1, you'll never see the tip of it. Your time is better spent appreciating the harmonic overtones of a fretless instrument

>>16054741
>doesn't mention equivalence classes
you get an F

>>16055458
I’m not talking about measurement. I’m talking about calculations in geometry. Are you retarded?

>>16054719
> sqrt(2) is both irrational and exists
its not a number though

>>16055821
No, just awakened

You require MMP to save your mind from the degradation of language

>>16057046
Geometry is a branch of mathematics, retard. Etymology doesn’t change that. What a midwit response

>>16055821
>>16057046
Take this cipher where ever you go, it will allow you to exist effortlessly in the modernists doublethinked academia, without having to be blinded to whats in front of your own eyes

Reject phonology, embrace etymology

>>16057061

>>16057061
All etymology is wrong if you go back far enough, and usually you can’t even go back further than a few thousand years

>>16057053
>I’m not talking about measurement. I’m talking about calculations in geometry. Are you retarded?
you realize how preposterous this sounds when geometry has -metry at the end right. means forming nouns related to measure. Your definition of geometry related neither to the earth (geo) or to measure (metry)

thats right, its as preposterous as using 'real' to denote "real numbers".

books separate man from beast -john dee

>>16057073
It’s a field of mathematics, regardless of etymology. In Chinese it has a different etymology, but it’s the same field. In Arabic it has a difference etymology, but it’s the same field. Is this difficult to understand for the retarded?

>>16057079
Some are so brainwashed by doublethink that they will fight to protect it, never realizing that if they were to learn, theyd look back in 6 months and realize they spent their entire life doing little better than mimicing the squeals of propagansists

Learn you language, the etymology ties meaning beyond just simply english

And please reject real numbers so we can have real music again

>>16054129
you sound like such a colossal pseud

>>16057091
>learn you language
Pathetic retard. Fuck off

>Go to school
>In math class
"So kids, lets take one of the most basic geometrical constructions possible! The diagonal of a square is the square root of 2 and ummm...well, we can never precisely measure it!"
>Wait...WHAT? Hang on what the hell does this...?
"Its an irrational number that just keeps on going off into infinity without ever repeating itself!"
>WHAT THE LIVING FUCK? There is something not quite right about all of this....
"Okay class, lets move on now...."

So little 12 year old me just goes with the flow, but at the back of mind there is always this nagging doubt, that there is something fundamentally flawed about mathematics. Something so deeply conceptual that even the most brilliant minds lack the cognitive abilities to discern the error. God, I wish I could figure this out. But I am not brilliant. Not even particularly clever. So I just live with it.
>Well, we have lived with it for 2000+ years and nobody else has come up with anything better, so just live with it. After all many people happily lived with the idea that the Earth was flat for centuries. Some still do.

>>16057105
Struck a chord, your qualms r3st witj those ylu tqught u geometry doesnt mean measuring the earth

>>16057097
Mod math is just vortex math without magnitude.

Get your degree before LARPing on the internet youre qualified to audit credentials.